A dual-purpose FIV-based hydroelastic energy harvesting and cylinder response suppression strategy that functions based on the synergy of piezoelectric and electromagnetic transduction (EMT) mechanisms is proposed and numerically implemented. The hybrid harvester consists of a linearly sprung (1DOF) square cylinder fitted on the wake side with a thin flexural-mode cantilever bimorph piezoelectric (PVDF) splitter plate in real-time collaboration with a transversely hooked induction-based magnet-coil type transducer. The Reynolds averaged Navier–Stokes (RANS) equations with the shear stress transport (SST) k-ω turbulence closure model are selected for qualitative/quantitative prediction of hydrodynamic flow behavior in a relatively wide Reynolds numbers range. Numerical simulations show that increasing Reynolds number for the single-alone EMT-equipped cylinder in the low to intermediate range (2×103≤Re≤3×104) can noticeably improve the system hydrokinetic energy harvesting performance where a distinct coupled VIV/galloping effect is observed. Also, the hybrid piezoelectromagnetic harvester is capable of effectively suppressing the key response parameters and considerably increase the total system electrical output in an extended working bandwidth (3×104<Re≤4×105). In particular, in contrast to the conventional fixed-base cylinder configurations, maximum power extraction can be achieved over most span of the flexible piezoelectric splitter plate at Re=4×105 where the flapping oscillations of splitter plate synchronizes with the downstream alternating wake vortices.